# A container has a volume of 24 L and holds 32 mol of gas. If the container is compressed such that its new volume is 7 L, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

Oct 8, 2017

$22.667 \text{mol}$

#### Explanation:

$P V = n R T$
$\implies \frac{P}{T} = n \frac{R}{V}$

Here,
-${V}_{1} = 24 L$
- ${V}_{2} = 7 L$
- ${n}_{1} = 32 m o l$
- n_2=?
- ${P}_{1} = {P}_{2}$
- ${T}_{1} = {T}_{2}$

As, ${P}_{1} / {T}_{1} = {P}_{2} / {T}_{2}$,

$\frac{{n}_{1} \cancel{R}}{{V}_{1}} = \frac{{n}_{2} \cancel{R}}{V} _ 2$

$= \frac{32 \text{mol}}{24 L} = \frac{x}{7 L}$

$= \frac{32 \text{mol}}{24 \cancel{L}} \cdot \left(7 \cancel{L}\right) = x$

$\implies x \approx 9.33 \text{mol}$. Is the new amount of moles...

Moles of gas to be released :
$= 32 \text{mol"-9.33"mol"=22.667"mol}$